In sequential clinical trials an objective is to treat the patients in the trial as effectively as possible. The project will be to develop near optimal designs for conducting a trial in which there are two or more competing treatments that have dichotomous responses. The case in which there are a fixed number of patients and the case where the number of patients is regarded as infinite with future patients discounted will both be considered. The research will draw heavily on previously published theoretical work by the principal investigator in which optimal designs are partially characterized when two treatments are available. A dynamic programming approach will be used to compare the designs developed with the optimal designs.